In modem telecommunications, unshielded twisted pairs (UTP) are used on a massive scale. The lower price of this transmission system and already established infrastructure currently are the main advantages of phone lines over optical lines. In comparison with single carrier modulation, the benefits of multicarrier modulation (MCM) can be explained as that the capacity of a MCM for a band limited system is always greater than the capacity of a single carrier system if channel SNR is not constant. Among MCM systems for wired communications, only Discrete Multitone (DMT) is currently deployed. Another MCM technique of interest is Filtered Multitone (FMT) system but will not be discussed further.
DMT modulation has become an important transmission method for asymmetric digital subscriber lines (ADSLs) which provides a high bit rate downstream channel and a lower bit rate upstream channel over twisted pair copper wire. DMT divides the available bandwidth into parallel subchannels or tones. Bits and power are allocated to individual subchannels or tones of an Inverse Fast Fourier Transform (IFFT)/Fast Fourier Transform (FFT) to maximize the data rate for a fixed margin or to maximize the margin for a fixed data rate. The process of allocating bits and power to individual subchannels is referred to as bit loading.
In other words, an incoming serial bitstream is divided into parallel streams which are used to Quadrature Amplitude Modulation (QAM)-modulate the different tones. After modulation with an IFFT, a cyclic prefix is added to each symbol being transmitted. The use of a cyclic prefix (pre-pending the tail of a signal after the IFFT to the block to be transmitted) allows for simplified equalization at the receiver with equalizers if the channel memory is not larger than the length of the cyclic prefix. In this case, equalization simply reduces to multiplication by a complex number on a subchannel by subchannel basis to remove the effects of the channel. Effects of the channel which can distort a communications signal can include, but are not limited to, noise in general, signal loss or attenuation, and phase noise. A channel can include, but is not limited to, a twisted wire pair, a coaxial cable, a bundle of cables, optical waveguides, and wireless mediums such as RF communications in the form of over-the-air transmissions and satellite transmissions.
Equalization that includes multiplication by a complex number on a subchannel by subchannel basis can be achieved with a combination of an IFFT, channel, and FFT that results in a diagonal matrix relating to the input block of data that is transmitted to the received block of data, with the channel response as the elements of the diagonal. In other words, if the cyclic prefix is longer than the channel impulse response, demodulation of a signal can be implemented with a FFT, followed by a complex 1-Tap Frequency Domain Equalizer (FEQ) per tone to compensate for the channel amplitude and phase effects.
Equalizers are devices generally used in receivers to compensate for the effects on a channel that can be established between a receiver and a transmitter. Equalizers compensate for these effects mathematically. Equalizers can operate in the time domain or in the frequency domain. Time domain equalizers (TEQs) can shorten the impulse response of a channel and they can partially bandpass an incoming signal as well as filter out-of-band noise power. TEQs are generally adaptive in nature and its coefficients are usually trained during initialization. On the other hand, FEQs can compensate amplitude attenuation and phase shift in frequency domain of received signals due to the effect of a band-limited channel.
A long cyclic prefix, however, results in a large overhead with respect to data rate. A conventional solution for this problem is to insert a real T-tap time-domain equalizer (TEQ) before demodulation, to shorten the channel impulse response. Imperfectly shortened channel impulse responses can yield to intersymbol interference (ISI) between two successive symbols and intercarrier interference (ISI) between different carriers.
Conventional algorithms have been developed to initialize the TEQ. The TEQ-initialization can compute a TEQ such that a cascade of channel impulse response and TEQ forms a finite impulse response (FIR) channel with a length shorter than the cyclic prefix. This criterion leads to use of a minimum mean square error (MMSE) technique for demodulation. Further details of MSME techniques and DMT are generally described in a printed publication, “Per Tone Equalization for DMT-Based Systems,” authored by Van Acker et al. for the IEE Transactions on Communications, Volume 49, No. 1, Jan. 2001, the entire contents of which are hereby incorporated by reference.
Back to MCM systems in general, many conventional MCM systems operating on long loops have very limited data throughput. The data throughput is limited by severe attenuation and thermal noise even when water-filling algorithms are used. For long loops beyond 18 Kft Far End Crosstalk (FEXT) is the only significant crosstalk and the total “noise” is dominated by Additive White Gaussian Noise (AWGN), which is typically −140 dBm/Hz. Reducing the thermal noise, accurately estimating the equalizer to cancel the channel distortion, and increasing the throughput for these long loops are severe challenges.
To increase the data rate for a long-reach modem, one of the major problems is using ISI cancellation. By using the averaging techniques for the noise reduction, ISI cancellation can be accomplished. Further, in order to estimate the equalization coefficients accurately, thermal noise should be removed from the training signal. One of the methods to combat ISI is the MMSE equalization, which is based on the minimization of a cost function. In MMSE, although the equalizer coefficients are calculated to minimize the MMSE error, the accuracy of the equalizer is still compromised due to thermal noise. As the length of the channel increases, the system matrix may become ill conditioned. The inversion of a system matrix can become mathematically intricate and additionally if the matrix has nulls, it becomes non-invertible. Various MMSE equalizers based on similar schemes with different constrains suffer from the same problems.
In view of the foregoing, there is a need in the art for initializing a modem in a mathematically less complex or more simple manner and in a shorter period of time. There is also a need in the art for increasing the data rate for long distance reach over existing telephone lines.